Understanding Domain and Range

The video tutorial explains the concepts of domain and range in functions, using graph projections to illustrate how to determine them. It covers examples of different types of functions, including absolute value, rational, and square root functions, and discusses how to find their domains and ranges. The tutorial emphasizes understanding the behavior of functions along the x-axis and y-axis to determine these sets.

What is the domain of a function?

• The lowest point on the graph

• The set of all x-values or inputs

• The set of all y-values or outputs

• The highest point on the graph

How can the range of a function be visualized?

• As a shadow on both axes

• As a shadow on the y-axis

• As a shadow on neither axis

• As a shadow on the x-axis

What condition must be met for a relation to be a function?

• Every x-value can have multiple y-values

• Every x-value can have only one y-value

• Every y-value can have multiple x-values

• Every y-value can have only one x-value

What is the domain of the function f(x) = |x| - 1?

• All numbers except zero

• All real numbers

• All positive numbers

• All negative numbers

What is the range of the function f(x) = |x| - 1?

• From -1 to +infinity

• From 0 to +infinity

• From -infinity to 0

• From -infinity to +infinity

What is the domain of a rational function where the denominator is zero at x = 1.5?

• All real numbers except 1.5

• All negative numbers

• All real numbers

• All positive numbers

What happens to the value of a fraction as the denominator increases?

• It becomes undefined

• It approaches infinity

• It remains constant

• It approaches zero

What is the domain of the function with the expression 4x + 2 ≥ 0?

• x ≤ -1/2

• x ≥ -1/2

• x > 0

• x < 0

What is the range of a function that involves taking the principal square root?

• From -infinity to 0

• From 0 to +infinity

• From -1 to +1

• From -infinity to +infinity

What is the smallest value you can get when taking the principal square root?

• One

• Positive infinity

• Negative infinity

• Zero